Question

the LCM of two numbers is 9 times their HCF. the sum of LCM and HCF is 500. find the HCF and LCM of the two numbers

Answer 1

Given:-

LCM=9×HCF

LCM+HCF=500

To Find:-

The value of LCM?

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$\orange{\boxed{\blue{\underline{\green{\mathrm{Proof:-}}}}}}$

•Lets find out, HCF as LCM is already 9times the HCF(VALUE)

→LCM+HCF=500 [°•°GIVEN→LCM=9HCF]

→9HCF+HCF=500

→10HCF=500

→HCF=$\frac{\cancel{500}}{\cancel{10}}$

→HCF=50

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•Using HCF=50 in LCM+HCF=500

→LCM+HCF=500 [°•° HCF=50]

→LCM+50=500

→LCM=500-50

→LCM=450

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Answer 2

$\huge \red a \red n \red s \red w \red e \red r \over$

Given:-

• LCM:- 9×HCF
• LCM+HCF = 500

To Find:-

• The value of LCM

$\huge \green s \red o \orange l \green u \red t \green i o \red n \over$

LCM+HCF = 500

Given LCM = 9HCF

9HCF + HCF= 500

10 HCF = 500

$\: hcf = \frac{500}{10} = 50$

HCF = 500

• Using HCF= 50 in LCM + HCF = 500

• LCM+ HCF= 500 [HCF = 50]

• LCM + 50 = 500

• LCM = 500 - 50

• LCM = 450

$\huge hence \: verified$